Question 1040468
{{{y=x*4^x}}}
Find the derivative,
{{{dy/dx=4^x(x*ln(4))+4^x}}}
{{{dy/dx=4^x(x*ln(4)+1)}}}
So the sign of the derivative is controlled by,
{{{x*ln(4)+1}}}
So find when,
{{{x*ln(4)+1=0}}}
{{{x*ln(4)=-1}}}
{{{x=-1/ln(4)}}}
The function is decreasing when {{{x<-1/ln(4)}}}
The function is increasing when {{{x>-1/ln(4)}}}
and it has a minimum when {{{x=-1/ln(4)}}}
When {{{x=-1/ln(4)}}}
{{{y=-1/(e*ln(4))}}}
So the range is 
[{{{-1/ln(4)}}},{{{infinity}}})
.
.
.
*[illustration dfc1.JPG].